The 23-year-old will be out of contract in the summer but has been in excellent goalscoring form for the Gunners recently.
Wenger has spoken repeatedly of his intention to keep the England forward at the Emirates Stadium, and the Arsenal boss said at a press conference on Thursday morning: "We are talking.
"It is very difficult to be predictable in these kinds of situations but our desire is there to do it as quickly as possible and ready to do it."
Walcott has scored 14 goals across all competitions for Arsenal so far this season, already his best total in a single campaign since moving to the north London club from Southampton in 2006.
He is keen to operate as a central striker and proved his worth in that position with a hat-trick in the 7-3 victory over Newcastle at the Emirates last Saturday.
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